Tracking noise via dynamic systems with a continuum of states

Abstract

A system and method reduces noise in a time series signal. A primary signal including stationary and non-stationary noise is modeled by a dynamic system having a continuum of states. A secondary signal including time series data is added to the primary signal to form a combined signal. The generic noise in the combined signal is estimated from samples of the combined signal using the dynamic system modeling the generic noise. Then, the estimated generic noise is removed from the combined signal to recover time series data.

Description

STATEMENT OF GOVERNMENT INTEREST[0001]The invention described herein may be manufactured and used by or for the Government of the United States of America for governmental purposes without the payment of any royalties thereon or therefor.FIELD OF THE INVENTION[0002]This invention relates generally to signal processing, and more particularly, methods and systems for reducing noise in time series signals.BACKGROUND OF THE INVENTION[0003]In the prior art as shown in FIG. 1, a signal processing system 100 is generally modeled as follows. A dynamic system 110 generates a primary signal 111. The primary signal 111 as used herein is a dynamic time series, e.g. human speech.[0004]The primary signal 111 is subject 120 to a corrupting and additive secondary signal 121, e.g., stationary random, white or Gaussian noise, to produce a combined signal 122. Because the noise “looks” the same at any instant in time, it can be considered “stationary.” The problem is to substantially recover the prima...

AI Technical Summary

Benefits of technology

[0012]The complexity of the estimated distribution of the state of the system is reduced by sampling the predicted distribution of the state at time steps, locally discretizing the samples in a dynamic manner and propagating the thus simplified distributions in time. The non-linearity of the relation between the true and measured outputs of the system is tackled by locally linearizing the relationship around each sample of the states.

Problems solved by technology

Tracking dynamic systems with a continuum of states in an analytical manner becomes difficult when conditional densities of the combined signal 122 are mixtures of many component densities.

Unfortunately, this is the case in most real-world systems where speech is subject to both stationary noise, and dynamic or non-stationary noise, e.g., background conversation, music, environmental acoustics, traffic, etc.

First, the complexity of the estimated distribution for the state of the system, as measured by the number of parameters in the system, increases exponentially over time.

Both of these problems are encountered in continuous-state dynamic systems used to estimate time series data.

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